A compression apparatus of the aforedescribed type can be used in medicinal practice for the creation of a synthetic state of bloodlessness as an incident to some surgical intervention at the extremity which requires that the flow of blood to the extremity be interdicted. The apparatus is applicable to upper and lower extremities and may utilize a so-called double-chamber sleeve which is suitable also for intravenous local anesthesia. The compression pressure within the sleeve, therefore, is intended to prevent the incursion of blood to portions of the extremity distal to the compression sleeve for the duration of the surgical procedure or operation. The compression pressure level is generally within a certain range in conventional apparatus of this type with the disadvantage that from time to time an excessive pressure may be applied. Excessive pressures can result in the formation of lesions, pressure-induced weakening of the limb, and later onset of disorders.